R-layer Mode Theory (RLMT) XXXVII: Dynamics of the Exterior Geometry and the Spiky Expansion Front

This volume develops a dynamical and observational framework for the exterior geometry introduced in Volume XXXVI of the R-layer Mode Theory (RLMT). The 4D Universe is modeled as a projection of a higher-dimensional manifold whose tension field governs the anisotropic expansion rate. Variations in this tension field generate a “spiky” expansion front, providing a unified explanation for the Hubble tension, void expansion anomalies, reduced dark matter requirements in galaxy groups, and directional variations in the local Hubble flow. The manuscript derives the dynamical equations of the tension field, formulates the structure of the expansion front, and presents numerical reconstruction methods based on TRGB distance measurements. Observational predictions and implications for cosmology and fundamental physics are discussed.